How do you factor x^3 + x^2 -9x -9 by grouping?
1 Answer
Jun 30, 2016
(x+1)(x-3)(x+3)
Explanation:
Group the terms into 'pairs' as follows.
[x^3+x^2]+[-9x-9] now factorise each pair.
color(red)(x^2)(x+1)-color(red)(9)(x+1) We now have a common factor of (x+1) which can be 'taken out'
(x+1)(color(red)(x^2-9))........ (A)
color(red)(x^2-9)" is a " color(blue)"difference of squares" and is factorised in general as follows.
color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))
x^2=(x)^2" and " 9=(3)^2rArra=x" and " b=3
rArrx^2-9=(x-3)(x+3) Substitute these factors into (A)
rArr(x+1)(x^2-9)=(x+1)(x-3)(x+3) Thus
x^3+x^2-9x-9=(x+1)(x-3)(x+3)
